Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Quantitative Aptitude for Banking Preparation

UPSC : Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

The document Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev is a part of the UPSC Course Quantitative Aptitude for Banking Preparation.
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Areas

Areas of some well-known figures are given below:

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRevMensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRevMensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRevMensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev
Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev 

Example.1 A horizontal pipe for carrying floodwater has a diameter of 1 m. When water in it is 10 cm deep then the width of water surface AB is equal to ________ cm.

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev
(1) 10 cm 
(2) 25 cm
(3) 60 cm 
(4) 70 cm
(5) None

Correct Answer is Option (3).

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

  • Let O be the centre of circle.
  • In ΔOAD
    ⇒ 502 = 402 + x2
    ⇒ 2500 – 1600 = x2
    ⇒ x2 = 900
    ⇒ x = 30
  • ∴ AB = 2x = 60 cm. 

Try yourself:The area of quadrilateral PQRS is 228cm2. Find the length of QA.
Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev
View Solution
 


Example.2 Area of the shaded region is:
Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

 Correct Answer is Option (1).

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

 

Volume

Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRevMensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRevMensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

 

Length of a Diagonal

  • The length of diagonal of a cuboid =  Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev
  • The length of a diagonal of a cube = Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

 

Example.3 An insect is crawling to climb a 20 metre long pipe of diameter 3.5 metres. If the insect take 4 circular rounds to reach the top of the building, then what will be total distance (in nearer metres) traveled by insect to reach the top?
(1) 47 m 
(2) 48 m 
(3) 49 m 
(4) 50 m

  • Since the insect is moving in circular way, so it will cover the distance which will be 4 times the distance of the longest side AB of a right angled triangle. In the figure AO is equal to the circumference of the pipe.
    AO = πd = Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev  = 11m
    BO = 5 m
    AB = Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev = Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev = 12.08 m
  • Total distance traveled = 12.08 × 4 = 48.32 m
  • Hence distance in nearer meters = 48 m
    Mensuration - Examples (with Solutions), Geometry, Quantitative Reasoning Quant Notes | EduRev

Try yourself:What is the volume of a cone having radius of 21cm and height of 5cm?
View Solution

 

Example.4 The surface area of a cube is 726 sq metres. Find the volume of the cube
(1) 1234 m2 
(2) 1431 m2
(3) 1341 m3 
(4) 1331 m3 
(5) None of these

Correct Answer is Option(4).

  • Surface area S = 726 m2 Volume V = ?
  • In a cube,
  • S = 6a2 = 726 ⇒ a2 = 121 ⇒ a = 11 m
  • So, V = a3 = 113 = 1331 m3.
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